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XYLENE POWER LTD.

FNR REACTIVITY

By Charles Rhodes, P.Eng., Ph.D.

INTRODUCTION:
The FNR reactivity as a function of temperature and hence its primary liquid sodium surface operating temperature is set by adjusting the amount of insertion of mobile fuel bundles into the matrix of slightly wider fixed fuel bundles. The following diagrams show a line of 9 fixed fuel bundlles separated by 8 slightly narrower mobile fuel bundles. The mobile fuel bundles are inserted into the bottom of the fixed fuel bundle matrix. On these diagrams the shrouds separating the fixed and mobile fuel bundles appear as thin black lines, core fuel portions of the fuel bundles are shown in red, the blanket portions of the fuel bundles are shown in green, the plenum portions of the fuel bundles are shown in light blue and the fuel tube end caps appear as solid black.

When the reactor is in cold shutdown the lower ends of the mobile fuel bundles are 1.2 m below the bottom of the matrix of fixed fuel bundles. As shown on the following diagram when the reactor is in cold shutdown the core fuel portions of the fixed and mobile fuel bundles are well separated and are isolated from each other by neutron absorbing U-238 in the blanket fuel, shown in green, which hold the reactor sub-critical.

When the reactor is operating with new fuel (20% Pu, no fission products) the mobile fuel bundles are partially inserted into the matrix of fixed fuel bundles. That partial insertion causes the mobile bundle core fuel to partially overlap the fixed bundle core fuel which causes the reactor to become critical. Once critical the reactor reactivity is controlled by thermal expansion of the fuel. The following diagram shows the relative positions of the fixed and mobile fuel bundles when the reactor is operating and the fuel has recently been reprocessed.

As the fuel ages the plutonium concentration in the core fuel gradually drops and the fission product concentration in the core fuel gradually rises. To compensate for this fuel aging mechanism the mobile fuel bundles are gradually further inserted into the fixed fuel bundle matrix to maintain the design primary liquid sodium surface temperature. This further insertion reduces the fraction of fission neutrons which diffuse out of the reactor core and are absorbed by the reactor blanket. When the reactor fuel has aged to the point that it is due for reprocessing the plutonium concentration in the core fuel has dropped to about 12.7% Pu and the core fuel portion of the mobile fuel bundles nearly fully overlaps the core fuel portions of the fixed fuel bundles as shown in the following diagram. In this state the mobile fuel bundles are fully inserted into the matrix of fixed fuel bundles. When the fuel requires reprocessing the primary liquid sodium surface temperature will fall below its design value in spite of full insertion of the mobile fuel bundles.


 

ASSEMBLY OF FUEL BUNDLES:
Note that fuel bundles are added to or removed from the assembly of FNR fuel bundles from the side, not from the top, so that during fuel bundle insertion or removal it is not necessary to pass the core portion of a mobile fuel bundle past the core portions of immediately adjacent fixed fuel bundles.
 

THERMAL POWER CONTROL:
In a liquid sodium cooled FNR the primary means of thermal power control is fuel thermal expansion which changes the local reactivity. As the reactor core zone fuel temperature rises above its setpoint fuel thermal expansion will cause the core zone reactivity to drop below unity which turns off the chain reaction. Note that as the reactor thermal load increases the fuel temperature increases which shuts down the chain reaction. In effect the FNR maintains a constant average fuel temperature. At maximum thermal load the liquid sodium surface temperature may drop by as much as 20 degrees C below its minimum load value.
 

MIDDLE CORE ZONE:
The middle core zone is the region where core fuel rods in fixed fuel bundles overlap core fuel rods in mobile fuel bundles.
[Middle core zone thickness]
= [0.9 m - (Mobile fuel bundle withdrawn length)]

Thus the middle core zone length varies from 0 m to 0.9 m. However, to obtain a net reactivity of unity the minimum overlap length is about 0.35 m.

In the reactor on state the middle core zone is super critical. The rate of neutron production in the middle core zone precisely equals to the rate of neutron absorption in the middle core zone plus the rate of neutron diffusion out of the middle core zone into the blanket zones. Hence to prevent prompt neutron criticality the middle core zone must not be too thick.

In practice during reactor turn-on the middle core zone thickness is gradually reduced until the reactor becomes critical. The liquid sodium temperature will then rise until the reactor becomes subcritical. Then the middle core zone thickness is again slightly reduced until again the liquid sodium temperature rises to make the reactor subcritical. This procedure is repeated over and over again until the liquid sodium temperature reaches its desired set point. If the reactor design is correct the desired liquid sodium operating temperature will be reached when the middle core zone is 0.45 m and the Pu weight fraction in the core fuel rods is 20%.

As the core fuel ages to maintain the desired liquid sodium operating temperature the middle core zone thickness must be gradually increased to ultimately become 0.9 m when the Pu weight fraction in the core fuel has fallen to about 12.5%.
 

UPPER CORE ZONE:
[Upper core zone thickness] = [0.9 m - (middle core zone thickness)]

[Upper core zone average fertile fuel concentration]
= [460 /(460 + 312)] [Middle core zone fertile fuel concentration]
 
= [115 /(193)] [Middle core zone fertile fuel concentration]

In the upper core zone there is neutron gain but not enough to sustain a chain reaction.
 

UPPER BLANKET MINIMUM THICKNESS:
[Upper blanket minimum thickness]
= [1.8 m - (Upper core zone thickness)]
= 0.9 m + (middle core zone thickness)
 

LOWER CORE ZONE:
[Lower core zone thickness] = [0.9 m - (middle core zone thickness)]

[Lower core zone average fertile fuel concentration]
= [312 /(460 + 312)] [Middle core zone average fertile fuel concentration]
 
= [78 /(193)] [Middle core zone fertile fuel concentration]

In the lower core zone there is neutron gain but not enough to sustain a chain reaction.
 

LOWER BLANKET MINIMUM THICKNESS:
[Lower blanket minimum thickness]
= [1.8 m - (Upper core zone thickness)]
= 0.9 m + (middle core zone thickness)
 

OPTIMUM REACTOR MODULATION:
The optimum reactor modulation will occur when the average fissile concentration in the upper core equals the average fissile concentraion in the lower core. Hence if the Pu fraction in the lower core rods is 20% the Pu fraction in the upper core rods should be:
20% (312 / 460) = 13.565%.

Then when the fuel is fresh the average Pu weight fraction in the middle core rods would be:
[0.2 (312) + 0.13565 (460)] / [312 + 460]
= 0.4 (312) / 772
= 0.16165

When the fuel is due for reprocessing the Pu weight fraction would be about:
0.16165 (12.5% / 20%) = 0.10104
We must examine the reactor material distribution to determine if the middle core zone will remain super critical at this average Pu fraction in the core rods.
 

REACTOR OFF:
When the reactor is off the mobile fuel bundles are 1.2 m withdrawn.

In the reactor off state:
Middle core zone thickness
= 0.9 m - 1.2 m
= - 0.3 m

In the reactor off state there must be absolute certainty that the chain reaction will stop regardless of the liquid sodium temperature.

The fuel bundles are engineered such that with the mobile fuel bundles 1.2 m withdrawn all core zones are sub-critical. Ideally if a single active fuel bundle in an array of active fuel bundles with their control portions withdrawn has its control portion fully inserted that fuel bundle should remain subcritical. This feature is necessary to prevent problems if a single fuel bundle jams in its fully inserted position.

In the reactor off state the fissile fuel density in the upper core zone is same as in the reactor on state. Hence this fissile fuel density must be subcritical.

In the reactor off state the fissile fuel density in the lower core zone is same as in the reactor on state. Hence this fissile fuel density must also be subcritical.

In the reactor off state the fissile fuel density in the middle core zone should be zero.
 

SUMMARY:
Proper reactor operation is highly dependent on maintenance of the correct middle core region thickness.
 

REACTOR MATHEMATICAL MODELLING:
We must solve the diffusion equation to find the diffusion fluxes of neutrons from the core region into the adjacent blanket regions in terms of the core dimensions. These mathematical solutions are presented at:
FNR CORE and at FNR BLANKET.
 

PLUTONIUM DOUBLING TIME:
An issue of great importance in large scale implementation of FNRs is the FNR run time required for one FNR to breed enough excess Pu-239 to allow startup of another identical FNR. This time may be calculated using the approximation that each plutonium atom fission releases of 3.1 neutrons of which 2.5 neutrons are required for long term sustaining reactor operation leaving 0.6 neutrons for breeding extra Pu-239. Thus one atom of Pu-239 has to fission to form 0.6 atoms of extra Pu-239.

In one reactor cycle time 15% of the fuel weight fissions, which is 3 / 4 of the initial plutonium weight.

Thus in one reactor cycle time the fractional increase in Pu is:
0.6 (3 / 4) = 0.45

Thus the plutonium doubling time is:
(1 cycle time) / 0.45
= 2.22 cycle times

If one cycle time = 30 years then:
Pu doubling time = 2.22 (30 years)
= 66.67 years

This is the time required for one FNR to form enough excess Pu to enable starting another FNR. Clearly this doubling time is too long to enable rapid deployment of FNRs.

With large scale implementation of FNRs the available supply of plutonium and trans uranium actinides will soon be exhausted. Hence the issue of the Pu-239 doubling time physically constrains the rate of growth of the FNR fleet.

Thus FNRs are viable for disposing of transuranium actinides but due to the Pu-239 doubling time will not in the near future provide enough power capacity for complete displacement of fossil fuels.
 

FNR REACTIVITY TRIMMING:
The neutron gain per fission step in an operating FNR can be expressed in the form:
Gf X Fc X Exp(- Vn Sigmaf Nf - Vn SigmaU Nu - Vn Sigmas Ns - Vn Sigmai Ni - Vn Sigmac Nc) ~ 1
where:
Gf = 3.1 neutrons out / neutron in = ideal fission neutron gain for Pu-239
Fc ~ (1 / 2) = fraction of neutrons produced that remain in the core rather than diffusing into the blanket
Vn = fast neutron velocity
Sigmaf = Pu-239 fast fission cross section
Nf = average Pu-239 atom concentration
Sigmau = U-238 fast neuton absorption cross section Nu = average U-238 atom concentration
Sigmas = sodium atom fast neutron absorption cross section
Ns = average sodium atom concentration Sigmai = iron fast neutron absorption cross section
Ni = average iron atom concentration
Sigmac = chromium atom fast neutron absorption cross section
Nc = average chromium atom concentration

During the working life of a fuel bundle operated to 15% burnup the Pu fraction drops from 20% to about 12.5%. Thus Nf varies from its initial value of Nfo to its final value of 0.625 Nfo. To maintain a reactivity of ~ 1.0 it is necessary to compensate for the change in Nf by increasing Fc which is adjusted by further insertion of mobile fuel bundles. Thus most of the nuclear heat is injected into the middle core zone. A related issue is that Nfo can vary from fuel bundle to fuel bundle due to variations in the initial Pu atom concentration. A complication with this strategy is that the aging of each fixed fuel bundle is determined by the aging of the various adjacent mobile fuel bundles. Thus keeping track of the aging of each fixed fuel bundle is a complicated process.

This web page partially updated December 9, 2019

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